Average Error: 10.9 → 1.0
Time: 23.9s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -5.73706509850903537 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{elif}\;y \le 2.1176056747920741 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{1}{z - a} \cdot \left(y \cdot \left(z - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z - a} \cdot \left(z - t\right)\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -5.73706509850903537 \cdot 10^{-97}:\\
\;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\

\mathbf{elif}\;y \le 2.1176056747920741 \cdot 10^{-19}:\\
\;\;\;\;x + \frac{1}{z - a} \cdot \left(y \cdot \left(z - t\right)\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{z - a} \cdot \left(z - t\right)\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r391965 = x;
        double r391966 = y;
        double r391967 = z;
        double r391968 = t;
        double r391969 = r391967 - r391968;
        double r391970 = r391966 * r391969;
        double r391971 = a;
        double r391972 = r391967 - r391971;
        double r391973 = r391970 / r391972;
        double r391974 = r391965 + r391973;
        return r391974;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r391975 = y;
        double r391976 = -5.737065098509035e-97;
        bool r391977 = r391975 <= r391976;
        double r391978 = x;
        double r391979 = z;
        double r391980 = a;
        double r391981 = r391979 - r391980;
        double r391982 = t;
        double r391983 = r391979 - r391982;
        double r391984 = r391981 / r391983;
        double r391985 = r391975 / r391984;
        double r391986 = r391978 + r391985;
        double r391987 = 2.117605674792074e-19;
        bool r391988 = r391975 <= r391987;
        double r391989 = 1.0;
        double r391990 = r391989 / r391981;
        double r391991 = r391975 * r391983;
        double r391992 = r391990 * r391991;
        double r391993 = r391978 + r391992;
        double r391994 = r391975 / r391981;
        double r391995 = r391994 * r391983;
        double r391996 = r391978 + r391995;
        double r391997 = r391988 ? r391993 : r391996;
        double r391998 = r391977 ? r391986 : r391997;
        return r391998;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.9
Target1.2
Herbie1.0
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -5.737065098509035e-97

    1. Initial program 17.7

      \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
    2. Using strategy rm

    3. Applied associate-/l*0.6

      \[\leadsto x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]

    if -5.737065098509035e-97 < y < 2.117605674792074e-19

    1. Initial program 0.2

      \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
    2. Using strategy rm

    3. Applied associate-/l*2.0

      \[\leadsto x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]
    4. Using strategy rm

    5. Applied clear-num2.0

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{z - a}{z - t}}{y}}}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity2.0

      \[\leadsto x + \frac{1}{\frac{\frac{z - a}{z - t}}{\color{blue}{1 \cdot y}}}\]

    8. Applied div-inv2.1

      \[\leadsto x + \frac{1}{\frac{\color{blue}{\left(z - a\right) \cdot \frac{1}{z - t}}}{1 \cdot y}}\]

    9. Applied times-frac0.4

      \[\leadsto x + \frac{1}{\color{blue}{\frac{z - a}{1} \cdot \frac{\frac{1}{z - t}}{y}}}\]

    10. Applied add-cube-cbrt0.4

      \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{z - a}{1} \cdot \frac{\frac{1}{z - t}}{y}}\]

    11. Applied times-frac0.3

      \[\leadsto x + \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{z - a}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{\frac{1}{z - t}}{y}}}\]

    12. Simplified0.3

      \[\leadsto x + \color{blue}{\frac{1}{z - a}} \cdot \frac{\sqrt[3]{1}}{\frac{\frac{1}{z - t}}{y}}\]

    13. Simplified0.2

      \[\leadsto x + \frac{1}{z - a} \cdot \color{blue}{\left(y \cdot \left(z - t\right)\right)}\]

    if 2.117605674792074e-19 < y

    1. Initial program 21.5

      \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
    2. Using strategy rm

    3. Applied associate-/l*0.6

      \[\leadsto x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]
    4. Using strategy rm

    5. Applied associate-/r/2.9

      \[\leadsto x + \color{blue}{\frac{y}{z - a} \cdot \left(z - t\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5.73706509850903537 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{elif}\;y \le 2.1176056747920741 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{1}{z - a} \cdot \left(y \cdot \left(z - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z - a} \cdot \left(z - t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (/ (* y (- z t)) (- z a))))